Localising Information in Bandlimited Quantum Field Theory
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A deeply-held belief in fundamental physics is that interactions must happen locally. Despite the great success of local models, there are many indications that locality must be abandoned in a theory of quantum gravity. For example, this nonlocality may appear as a minimum length or an ultraviolet cutoff at the Planck scale. But without a full theory of quantum gravity, can we model the effect that this nonlocality may have on sub-Planckian physics? In this work, we study a model for an ultraviolet cutoff based on Shannon's sampling theorem of classical information theory. We apply the sampling theorem to quantum field theory, which results in the ability to represent fields on a lattice without breaking Euclidean symmetries. After building up the bandlimited quantum field theory, we study the locality and entanglement of its degrees of freedom. We find that each degree of freedom occupies an incompressible volume of space, on the order of the Planck scale in size.